Efficient Numerical Solution Methods for Dislocation based Plasticity

我们将开发三维单晶小应变弹塑性的有效近似和并行求解方法，其中塑性应变由研究组开发的平均连续位错密度（CDD）系统确定。在每个滑移系统中，将实现CDD模型的龙格-库塔不连续伽辽金方法，该方法描述了位错密度、GND密度矢量和曲率密度的演化。变形取决于由Orowan关系确定的塑性剪切应变，然后用有限元近似。我们的目标是为结合两个模型的整个系统的耦合提供一个鲁棒和稳定的算法，并允许使用全套滑移系统进行大规模模拟。CDD模型的数值实施将基于第一个资助期开发的数值方法，其中考虑扩展配置空间中的hdCDD模型；将完整模型和简化模型的结果与一个或两个活动滑动系统的二维减少进行比较。位错速度的物质规律，不同滑移系统之间的位错密度的相互作用，以及位错的适当边界条件将得到推导，然后与研究组的项目伙伴密切合作进行数值评估。

We will develop efficient approximations and parallel solution methods for single-crystal small strain elasto-plasticity in 3D, where the plastic strain is determined by the averaged continuum dislocation density (CDD) system developed in the research group. Within each slip system, a Runge-Kutta discontinuous Galerkin method for the CDD model will be realized, which describes the evolution of the dislocation density, the GND density vector, and the curvature density. The deformation, depending on the plastic shear strain determined by Orowan's relation, is then approximated with finite elements. We aim for a robust and stable algorithm for the coupling of the full system which combines the two models, and which allows for large-scale simulations with a full set of slip systems.The numerical implementation of the CDD model will be based on the numerical methods developed in the first funding period, where the hdCDD model in the extended configuration space is considered; the results of the full and the reduced models will be compared for a 2D reduction with one or two active slip systems.The material law for the dislocation velocity, the interaction of the dislocation densities between different slip systems, and appropriate boundary conditions for the dislocations will be derived then evaluated numerically in close cooperation with the project partners in the research group.